a-cosmology-group/acg#161

In any case and is good enough for a model that’s wrong anyway, why do you care?

Well… diligence I suppose. If we’re going to be looking at models, comparing them to the data seems important. And the Pantheon data has this “WARNING, DO NOT FIT COSMOLOGICAL PARAMETERS WITH THESE UNCERTAINTIES.”

So… what if I want to test the best fit to a different FLRW, or a non-FLRW model in my case.

I want to compare LCDM and my luminosity distance equation side by side against the Pantheon+SH0ES data.

I thought that the SSE described above would be a good way to do that.

So here’s some Javascript that downloads the data and parses it:

var snData = []
var url = "https://raw.githubusercontent.com/PantheonPlusSH0ES/DataRelease/main/Pantheon%2B_Data/4_DISTANCES_AND_COVAR/Pantheon%2BSH0ES.dat"
fetch(url).then(res => res.text()).then(text => {
    var lines = text.split("\n")
    for (var i = 1; i < lines.length - 1; i++) {
        var line = lines[i].split(" ")
        snData.push({
            z: parseFloat(line[2]),
            mu: parseFloat(line[10]),
            muerr: parseFloat(line[11]),
        })
    }
})

Now that you have the SN data loaded, pick a range for Hubble’s constant (say 60 to 80) and calculate the sum of squared errors:

var lowest
for (var H = 70; H < 75; H+=0.1) {
    var sse = calculateSSE(H)

    if (!lowest || lowest.sse > sse) {
        lowest = {H, sse}
    }
}
console.log(lowest)


function calculateSSE(H0) {
    var d, mu
    var err = 0

    snData.forEach(sn => {
        d = getModelLuminosityDistance(sn.z)

        mu = 5 * Math.log10(d) + 25

        err += Math.pow(sn.mu - mu, 2)
    })
    return err
} 

All you have to do is supply getModelLuminosityDistance(z).

So I can use the equation for my hypothesis, and I can use LCDM, and compare the results.

So my hypothesis is a better fit, but a nice amount. But…. this isn’t using the error margin from the SSE equation. It’s just:

err += Math.pow(sn.mu - mu, 2)

It should be:

err += Math.pow(sn.mu - mu, 2) / Math.pow(sn.muerr, 2)

When I do that, I get this.

And LCDM just inches out the hypothesis. That’s why I was wondering, the data has that warning to not use it to fit cosmological parameters. I’m wondering if that’s because MU_SHOES_ERR_DIAG is fine tuned for that model. In which case it might not make much sense to include it in my calculations. In which case, I’d like to use the right value for the error margins in the calculations.

If we’re going to be looking at models, comparing them to the data seems important.

I do support this statement. This was the consensus reached at the Second Crisis in Cosmology Conference. However data is always pre-processed by astronomers before publications in tables, and LCDM assumptions are used to derive the numbers.

So, while it is perfectly fine to use databases to test the LCDM model, LCDM assumptions might have to be removed from the database before attempting a fit to any other cosmological model.

Specifically for the fit you describe above, redshift data is obtained directly from spectra and not corrected, so it can be used safely. However, SNe luminosity $\mu$ is corrected for all sorts of effects (dust absorption, evolution of the host galaxy, calculated absolute luminosity, etc.) based on LCDM models.

To get an accurate fit to your model you would need to redo the data analysis from scratch… Professional astronomer Martín López-Corredoira has done such analyses (see for example this paper and this one were the distance $(1+z)ln(1+z)$ is examined) but he also uses data processed with LDCM assumptions. The logarithmic model $(1+z)ln(1+z)$ doesn’t do too badly, but López-Corredoira’s conclusions are still biased by the LCDM assumptions that remain in the source data.

A correct re-analysis would require the development of new analysis tools that would replace decades of work in astronomy that produced data tainted with LCDM assumptions - a task that is too big for a single person.

Maybe one or two motivated people and a sufficiently trained AI/ChatGPT….

You have to look for someone who dosen’t use measurements based on LCDM